Critical Connections - Trace

Trace on input $n=4$, edges $[[0,1],[1,2],[2,0],[1,3]]$: DFS from $0$: disc[0]=0, low[0]=0. Visit $1$: disc[1]=1, low[1]=1. Visit $2$: disc[2]=2, low[2]=2. Back edge $2-0$: low[2]=0. Backtrack: low[1]=0.

Visit $3$: disc[3]=3, low[3]=3. Backtrack: check low[3]=3 > disc[1]=1, add $(1, 3)$ to result. Bridges: $[[1,3]]$. This is the only edge whose removal disconnects the graph.